Question

For the following exercise, solve each system by addition.

a. 7x−2y = 3
b. 4x + 5y = 3.25

Answer 1

The solution is x = 0.5 and y = 0.25.

Step-by-step explanation:

To solve the system of equations:

1. Start by multiplying equation (a) by 4 and equation (b) by 7 to make the coefficients of x in both equations equal:

• 28x - 8y = 12
• 28x + 35y = 22.75

Now subtract the first equation from the second equation to eliminate x:

• 28x + 35y - 28x + 8y = 22.75 - 12
• 43y = 10.75

Solve for y by dividing both sides of the equation by 43:

• y = 0.25

Substitute the value of y back into either equation to solve for x:

• 7x - 2(0.25) = 3
• 7x - 0.5 = 3
• 7x = 3 + 0.5
• 7x = 3.5
• x = 3.5/7
• x = 0.5

The solution to the system of equations is x = 0.5 and y = 0.25.